- #1

RJLiberator

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## Homework Statement

Let f,h ∈S_4 be described by:

f(1) = 1

f(2) = 4

f(3) = 3

f(4) = 2

h(1) = 4

h(2) = 3

h(3) = 2

h(4) = 1

Express (f°h) in terms of its behavior on {1,2,3,4} and then find the order of (f°h).

## Homework Equations

## The Attempt at a Solution

So, first I express (f°h) in terms of its behavior.

(f°h)(1) = 2

(f°h)(2) = 3

(f°h)(3) = 4

(f°h)(4) = 1

Done!

Now, find the order of (f°h):

The order of (f°h) is min{K:g^k-e} or infinity if no such k exists.

I'm having a bit of difficulty in this. To me, when I search wikipedia: https://en.wikipedia.org/wiki/Order_(group_theory)

It says that the order is the cardinality or the number of elements in the set.

(f°h)'s order thus is 4?

But I have a feeling it might be 3 based on in class examples.

My answer is 4.

How did I do?